Since the groundbreaking work of Einstein, gravitation is conceived as defining the geometry of spacetime - even defining the very concepts of time and space itself. Planetary motion as well as the motion of massless particles, that is to say light, become the straightest possible paths in a non-Euclidean geometry.

General relativity is a very successful theory. Its predictions range from the deflection of light by massive bodies which distort spacetime (Einstein-lensing) to that of gravitational radiation carrying away energy in the form of "ripples" in spacetime (Hulse-Taylor binary pulsar), as well as to the expansion of the universe (microwave background radiation). One of the most spectacular predictions of general relativity is the existence of black holes, which by now has been confirmed indirectly by numerous astrophysical observations.

Despite of these successes there are several unresolved problems in the physics of gravitation, some of which are considered as the biggest problems in contemporary theoretical physics:

  • The cosmological constant problem entails a gigantic discrepancy (123 orders of magnitude) between observation and naive theoretical expectation, and so far no satisfying explanation exists that resolves this discrepancy.
  • Numerous astrophysical and cosmological observations reveal discrepancies with the theory of general relativity, unless we postulate the existence of dark matter, which so far has not been detected in particle physics experiments.
  • The elusive theory of quantum gravity still is very much a theory under construction, with several conceptual and technical issues seeking for solutions.
  • General relativity predicts its own failure as a consequence of the famous singularity theorems. Physically this means that spacetime contains regions where the curvature grows without a bound. The most prominent examples are the singularities within black holes as well as the Big Bang singularity.

Deeper insights into the structure of physical systems have often been achieved by the imposition of symmetries. This usually breaks the problem down into simpler building blocks which ideally allow a complete solution. Gravity is no exception to this rule since the prototypic black-hole solution, the Schwarzschild geometry (actually the first exact non-trivial solution of the Einstein-equations), has been found precisely along theses lines, i.e. upon imposing spherical symmetry. It is therefore natural to pursue a similar plan of attack for the quantization of gravity. The corresponding models become gravitational theories in a 1+1 dimensional spacetime coupled to the area of the two-sphere which becomes a dynamical variable in the reduced theory. There are several other ways how lowerdimensional (1+1 and 2+1) models arise from higherdimensional configurations in string theory or general relativity, and the description of gravity in lower dimensions is one of the key research fields of our group.